“Recognising and spreading sophisticated pedagogical practice across our community so that students learn in better and more powerful ways...”
My professional inquiry is about "language in abundance", using subject-specific literacy strategies and constructivist teaching and learning explicitly through context to inform my teaching practice so that there is a shift in academic achievement of Maori Learners to meet our 2018 school target of 80% achieving NCEA L1 Numeracy.

Thursday, 9 February 2017

Lesson Sequence

Number

Fractions: addition and subtraction

Year 9

Teacher practice

Constructivist

Experiential

Differentiation

Teacher conferenced with various groups using student knowledge as a guide and answered all questions by probing and encouraging learners tocommunicate their thinkingcollaboratively so that they can do critical thinking and showcreativity as they learn (4 C’s for today’s Learners)

Learning Outcomes

Level 3: Use a range of additive and simple multiplicative strategies on fractions

Learners are successful if they can do basic multiplication and division of fractions and simplify where necessary

SOLO Taxonomy

Pre structural

Uni

structural

Multi

structural

Relational

Extended abstract

I need help

I can Identify

numerators and denominators

I can describe a procedure and do calculations with fraction problems in context

I can explain and organise my thinking to solve fraction problems in context

I can create and predict solutions and reflect on my answers

Do Now (Introduction)

Solve by using numbers and mathematical symbols

half of ten ½ x 10 = 5

one quarter of twelve ¼ x 12 =3

one fifth of twenty ⅕ x 20 = 4

Can you explain your thinking for each answer?

ten divided by two or 10/2 = 5

twelve divided by four or 12/4 = 3

twenty divided by five or 20/5 = 4

How can you write the number 12 as a fraction

Learners discuss or check online until they come up with a solution of

121

Explain three quarters of 12, but rewrite 12 as a fraction

3/4 x 12/1

3 x 12 divided by 4 x 1 = 36/4 = 9

Can we make a general rule when multiplying fractions?

Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction

Learners who immediately simplify 36/4 as 9 explain to their neighbour as to why they simplified the fraction

Find a Google image that reinforces your knowledge of multiplying fractions and explain

your learning to your neighbour.

Teacher provocation

Reread your general rule for multiplying fractions.

Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction

Using this knowledge, can we say that when dividing fractions we divide the numerators to get the top part of the fraction and divide the denominators to get the bottom part of the fraction?

Learners guess either yes or no and are given time to explore online for the rules when dividing

fractions before an example is discussed

When dividing fractions, we go to KFC Keep, Flip, Change

KEEP first fraction

FLIP the fraction to the right of the division sign

CHANGE division to multiplication

Then use your rule “Multiply the numerators to get the top part of the fraction then multiply the denominators to get the bottom part of the fraction”

Example

2/7 ÷ 3/4 becomes

Answer 2 x 4 = 8

7 x 3 21

An additional challenge was done using 3 fractions to reinforce the learning that we Keep the first fraction, Flip the fractions to the right of the division sign and then Change division to multiplication

Contextual challenge (card resource)

Mrs Dunn is creating a cut-out resource made from special paper. She has ⅔ of a page left and needs ⅙ of a page for each resource. How many cut-out resources can she make?

⅔ ÷ ⅙

⅔ x 6

12/3

4 cut-outs

Lesson sequence

Solving fraction x whole number

Solving fraction x fraction

Creating a rule when multiplying fractions

Exploring division of fractions

Division in context

Making learning visible and documenting evidence of learners’ understanding of multiplication and division of fractions by creating personalised notes, inserting images and explaining them to peers

Learning Experiences

Relating fractions to decimals

Exploring equivalent fractions

Developing and using strategies for multiplication and division of fractions

Teacher conferenced with various groups using learners knowledge as a guide and answered all questions by probing and encouraging learners to communicate their thinking collaboratively so

that they could do critical thinking and show creativity as they learned (4 C’s for today’s Learners)

Learning Outcomes

Level 3: Ordering decimals

Level 4: Decimals and place value to 3 places

Level 5: Recurring decimals (extension)

Success criteria:

Learners are successful if they can order decimals, read decimals correctly, compare decimals

and write decimals as percentages

SOLO Taxonomy

Pre structural

Uni

structural

Multi

structural

Relational

Extended abstract

I need help

I can Identify Decimals

in daily life

I can describe a procedure and do calculations with Number problems in context

I can explain and organise my thinking to solve Number problems in context

I can create and predict solutions and reflect on my answers

Do Now (Introduction)

Rearrange these letters “a decimal point” to explain what a decimal is. Use each letter only once and use all letters.

Teacher reads the instruction aloud and answers any questions posed by learners

Learners work independently and/or collaboratively as they work towards a possible solution

I’m a dot in place

Lesson sequence

Rearrange given letters to better understand what a decimal point is

If I gave you $500 would you be happy?

Now along comes the decimal point and lands just after the number 5 to make $5.00, would you still be happy? Class discussion about the impact of the decimal point on the value of the money

Answer question 1 and 2 to determine learners’ curriculum level

Question 1. Four friends, Mele, Tui, Tevita and Anna can jump 3.1m, 3.15, 3.01 and 3.10m respectively. Arrange these distances in ascending order

Teacher comment: When rearranging or comparing, decimals, look at the first digit, of each number: if they are similar, then look at and compare the next digit eg in 3.15 and 3.01 (1/10 is greater than 0/10 or 15/100 is greater than 1/100), so 3.15 is greater than 3.01

Thinking/discussion: When comparing 3.1 and 3.10 both can be read as having 1/10, so the two decimals are equal.

Any zero after the decimal point that is not followed by another number is just a place-holder

Question 2. Draw a number line (any length) from 0 to 1. Mark the middle and give it a decimal value. Keep finding the middle until you reach 3 decimal places.

Use your learning outcomes table, from Mrs Dunn Maths site to determine the curriculum level for each Question (this is for learners to identify their learning needs)

Teacher provocations

How would you read this decimal 1.25?

one and twenty- five hundredths

one and two tenths and five hundredths

one point two five not one point twenty five - Learners work independently and/or collaboratively

Teacher provides opportunities for learners to develop and demonstrate their thinking by discussing with peers and documenting on a Google doc. Teacher expectation is that of learners’ managing their learning.

Learners self-manage by choosing the appropriate curriculum levels for the topic and can move on to the next level if they feel confident in their ability

Learners show evidence of their thinking and learning by creating personalised notes after navigating the hyperlinked Decimals resources on Mrs Dunn Maths site

All evidence of thinking/learning is visible on a Google document which is shared with the teacher and can also be shared with peers for commenting

Learning Experiences

Learners work independently and/or collaboratively. Writing decimals in words and symbols as learners often confuse decimals with money and read it incorrectly.

Learners work independently and/or collaboratively. Comparing decimals on number lines to see progressions from smallest to biggest

Convert common Decimals up to 2 dp) to Fractions (L3) which will lead on to basic operations with fractions (L4,5 )

Daily life

Fractions are used in baking or cooking. Basic operations are used eg if ¼ cup of sugar, sometimes it is necessary to either double or halve the recipe.

Reflection

More emphasis needs to be placed on place value, particularly for numbers after the decimal point so that learners use words like tenths, hundredths and thousandths confidently. Using money as an example when learning about decimals is contradictory as $5.70 (five dollars seventy) is not read as five point seven zero dollars. There are no tens, hundreds and thousands after the decimal point; instead it is tenths, hundredths and thousandths

Number

Fraction, Decimal, Percent Conversion

Year 9

Teacher practice

Constructivist

Experiential

Differentiation

Teacher conferenced with various groups using learner knowledge as a guide and answered all questions by probing and encouraging learners tocommunicate their thinkingcollaboratively so that they can do critical thinking and showcreativity as they learn (4 C’s for today’s learners)

Learners are successful if they can convert commonly used Fraction, Decimal and Percent and can work out prices regardless of whether discounts are expressed as Fractions or Percentages

SOLO Taxonomy

Pre structural

Uni

structural

Multi

structural

Relational

Extended abstract

I need help

I can Identify

Fractions, Decimals and Percent

I can describe a procedure and do calculations with Number problems in context

I can explain and organise my thinking to solve Number problems in context

I can create and predict solutions and reflect on my answers

Do Now (Introduction)

On weekends or after school, where do you see Fractions and/or Percent? Online activity

A few volunteers explain what they wrote on the lino board while the rest of the class listens attentively and respectfully

Lesson sequence

Question 1. Retailers express some of their discounts as Fractions and others as a Percent. Explain how to determine which discount will benefit you the most?

Briscoes is offering a 25% discount on a $20 fan and The Warehouse is one third discount on a $30 fan.

Which retailer is offering you a better buy and how much change will you get if you pay with a $50 note.

Statement

Working

Answer

Briscoes discount

25% x $20

$5

Cost at Briscoes

$20 - $5

$15

Change at Briscoes

$50 - $15

$35

Warehouse discount

⅓ x $30

$10

Cost at Warehouse

$30 - $10

$20

Change (Warehouse)

$50 - $20

$30

⅓ is bigger than 25% (¼) so Better deal is at The Warehouse

Activity 1

*Screenshot a house on the internet that you would like to buy.

a) How much is the house?

b) Write this amount in words. (Level 3)

c) What will the ⅕ deposit be? (Level 4)

d) How much will still be owing? (Level 3)

Real estate commission in Auckland ranges from 2.95 - 4% for the first $300 000 and then 2 - 2.5% thereafter. A base fee up to $500 is charged regardless of whether the house is sold or not. GST is also added.

e)How much commission would be made if you sold your house at the price mentioned in (a) (level 5)

Learning Experiences

Learners work independently and/or collaboratively by adding their contribution to the lino activity about where they see Fractions and/or Percent.

Chunking - break information up into smaller pieces or chunks to facilitate understanding

Word definition

Word

My definition

Online definition

discount

less

deduction from the usual cost of something

percent

100

one part in every hundred

commission

don’t know

money paid upon completion of a task

retailer

not sure

business or person who sells goods to consumers

deposit

money that you put down

first instalment with the balance being paid later

Sharing learning

Teacher comments on personalised learners docs and their blogs

Learners blog their learning experience and comment on peers blogs

Next steps

Curriculum

Integers

Daily life

Daily temperatures

Credit and debt

Sea level (height above and below)

Reflection

Much enthusiasm was generated as learners compared their selected home with peers and some even ventured to homes in other countries - this will lead to exchange rates and ratio at a later stage

Number

Integers

Year 9

Teacher practice

Constructivist

Experiential

Differentiation

Teacher conferenced with various groups using student knowledge as a guide and answered all questions by probing and encouraging learners tocommunicate their thinkingcollaboratively so that they can do critical thinking and showcreativity as they learn (4 C’s for today’s learners)

Learning Outcomes

Level 4: Understand addition and subtraction of integers.

Know the relative size and place value structure of positive and negative

numbers

Level 5: Understand operations on integers

Success criteria

Learners are successful if they can understand the size and place value of integers and can understand operations on integers

SOLO Taxonomy

Pre structural

Uni

structural

Multi

structural

Relational

Extended abstract

I need help

I can Identify

I can describe a procedure and do calculations with Integer problems in context

I can explain and organise my thinking to solve Integer problems in context

I can create and predict solutions and reflect on my answers

Do Now (Introduction)

Google today’s temperature in Auckland.

240C

Choose a country or city in the Northern hemisphere and write down their temperature. Use Google maps if you need help finding a city or country.

Russia, -20C. Discussion about why other countries are not as warm as Auckland.

The use of images hooked learners into understanding what integers are and the use thereof; particularly the use of integers in daily life

Number

Number in context

Year 9

Teacher practice

Constructivist

Collaboration

Teacher conferenced with various groups using student knowledge as a guide and answered all questions by probing and encouraging learners tocommunicate their thinkingcollaboratively so that they can do critical thinking and showcreativity as they learn (4 C’s for today’s learners)

Learning Outcomes

Level 3: Describe a procedure and do calculations with Number problems in context

Level 4: Explain and organise thinking to solve Number problems in context

Level 5: Create and predict solutions and reflect on answers

Success criteria

Learners are successful if they can solve number problems in context

SOLO Taxonomy

Pre structural

Uni

structural

Multi

structural

Relational

Extended abstract

I need help

I can Identify

I can describe a procedure and do calculations with Number problems in context

I can explain and organise my thinking to solve Number problems in context

Attempt and solve a contextual task to give learners an indication of their achievement

Trip to Wellington

24 students in 9KLe were planning a trip to Wellington in September with the lovely Mr Mansell. The cost of the trip was $80 per student. The group had a sausage sizzle to raise funds. They needed 8 loaves of bread. Elstree Dairy had bread for $2.20 each, but the owner gave them a 15% discount. Students also bought $50 worth of sausages. Onions and tomato sauce were donated by the Geek Cafe. Students sold 110 sausages for $1.50 each and then had a bake sale a few days later. All baked goods were donated and students made a profit of $250. Mrs Dunn offered to donate ⅕ of the amount raised at the bake sale. How much would each student have to pay?